Dynamically supported AMVs cannot be operated comfortably at high speeds in or above rough water. Examples of such AMVs include air cushion vehicles, surface effect ships, wing in ground effect ("WIG") aircraft, and hydrofoil craft.
Hydrofoil craft are boats which typically possess a more or less conventional planing boat hull and which have one or more vertical struts extending from beneath the hull into the water. Each vertical strut typically carries at least one foil. When the hydrofoil craft has accelerated to a sufficient velocity through the water, the lift created by the foils raises the hull above the water's surface, thus eliminating the hull's resistance.
WIG aircraft, in contrast, are "flying boats" intended to cruise just above wave crests so as to avoid all but very occasional water contact during flight. WIG aircraft possess one or more wings which are generally three orders of magnitude larger than the foils of hydrofoil craft. When a WIG aircraft has accelerated to a sufficient velocity through the water, the aerodynamic lift created by these wings lifts the aircraft entirely out of the water. By remaining close to the water's surface, WIG aircraft encounter significantly less resistance than they would encounter at higher altitudes because their aerodynamic lift is much greater closer to the water's surface than it would be at higher altitudes.
Hydrofoils are often used to transport people and cargo across varying sea states However, hydrofoils are typically used in rough water only at reduced speeds. WIG aircraft have not yet been built commercially.
To determine how a hydrofoil craft could be operated at high speeds in rough waters without resulting in an uncomfortable ride, I engaged in a "time-domain analysis" in which the actual forces on a craft were calculated at successive time intervals. From these calculations, the craft's motion in space could be determined.
I performed a time-domain computer analysis to reconstruct the detailed shape of a random sea's surface (i.e., the random wave patterns), as a function of both time and space. The real random seas which are actually experienced can be thought of as the sum of many sinusoidal component waves where each individual wave component has its own orbital velocity A reconstruction of such a random sea was obtained by using wave components of equal energy rather than wave components of equal frequency in the method described in Principles of Naval Architecture, Society of Naval and Marine Engineers, Chp. 8 (1990). The resulting random seaway was found to follow the statistical theories postulated in Cartwright, D. E., and Longuet-Higgins, M. S., "The Statistical Distribution of the Maxima of a Random Function," Proc. Rov. Soc., Ser. A, Vol. 237, pp.212-232 (1956).
Once realistic random seas could be computed, the water's movement and velocity below the water's surface could be studied. During this study, I discovered that the velocity of water in a seaway typically approximated the expected value for a sinusoidal wave train of the same average wave height and length. Periodically, however, the individual wave components would combine such that the aggregation of the components would result in much more or much less vertical velocity than would be the case for a single sinusoidal wave.
I believe that these occasionally extreme changes in vertical water velocity are at least partially responsible for the uncomfortable and sometimes injurious rides to which hydrofoil craft are subject in rough water, particularly when the occasionally extreme change in water velocity is a "downgust". When a foil is moving horizontally in the water and encounters such a downgust, the effect of this downgust, from the foil's point of view, is the same as if the foil were lifted rapidly upward. In either case, the "added mass" of the water in the vicinity of the foil imposes a large downward acting load on the foil.
The concept of "added mass" has been known to hydrodynamicists for at least two centuries, but is not well understood by most engineers. I have described the phenomenon in some detail in the first and second chapters of my book "Design of High Speed Boats: Volume 1, Planing", published by Fishergate, Inc., 2521 Riva Road, Annapolis, Md. 21401.
Roughly speaking, a submerged body (such as a foil) moving through the water displaces the water locally by its passage. The water is moved aside as the foil pushes by, and then more or less returns to where it was after the foil has passed. If the foil is moving at a constant speed, this movement of the water in its vicinity does not cause any resistance to the foil's motion. The resistance which does exist is due to the water's viscosity.
When the foil is accelerating to higher speeds, however, this moving aside of the water provides additional resistance to the acceleration, and so we call this effect "added mass". A given propulsive force causes the foil to accelerate less rapidly in water than it would in air, because of this added mass which is three orders of magnitude greater in water than in air because of water's much greater density. Conversely, the hydrodynamic force exerted on a foil, if the water is accelerating, is larger than its constant speed resistance.
Very roughly, the "added mass" of a high aspect ratio body like a foil is equal to the mass of water in a circular cylinder whose length is equal to the foil's span and whose diameter is equal to the foil's thickness or breadth measured at right angles to its direction of motion. Thus, if a foil has a span of ten feet, a chord of four feet and a thickness of 0.3 feet, its added mass for motion parallel to its chord will be about ##EQU1##
If, on other hand, its motion is at right angles to the chord, its added mass will be about ##EQU2##
Thus, although the "added mass" is not important for a foil's normal motion roughly parallel to its chord, it has a powerful effect on any vertical motion which may be superimposed on this generally horizontal motion. The added mass resists upward and downward acceleration of the foil. Conversely, it the water is accelerating vertically at ten feet per second per second (ft/sec.sup.2), the vertical force on the foil, due to "added mass" alone, will be about EQU 251.3.times.10=2,513 pounds EQU (mass).times.(acceleration)=(force)
Notice that this effect has nothing to do with the foil's angle of attack to the relative flow of water, so that it is not significantly influenced by changing the foil's angle to the flow.
Accordingly, when a hydrofoil craft encounters a downgust and tries to compensate for this downgust by changing the angle of incidence of its foils to increase lift, this compensation by itself is not sufficient to overcome the substantial downward impulse due to the water's added mass. In other words, merely changing the angle of incidence of the foil will not prevent a downgust of water from forcing the foil farther below the water's surface than it was prior to encountering the downgust. When the foil is attached to a conventional vertical strut which is rigid, the downgust of water will necessarily lower the hydrofoil craft's hull as well as the foil. If the downgust of water is sufficiently large, the craft's hull can be lowered enough so that the hull will impact the water's surface ("plough-in"), which is uncomfortable and occasionally dangerous.
U.S. Pat. Nos. 3,417,722 (O'Neill), No. 2,771,051 (Von Schertel) and No. 3,141,437 (Bush, et al.) are examples of previous efforts made in an attempt to create a hydrofoil craft which could operate at higher speeds in rough water. However, these three patents tried to solve this problem by merely changing the foil's angle of incidence to compensate for any changes in the orbital velocity of waves. As is alluded to previously, these attempts were unsuccessful because they did not take into account the "added mass" effect of the vertically moving water. Furthermore, merely "changing the [foil's angle of incidence] in an attempt to maintain an essentially constant angle of attack in waves is a self-defeating process [because] the inherent lags in the total system make this a practical impossibility." Ellsworth, W., "Hydrofoil Development--Issues and Answers," AlAA/SNAME Advanced Marine Vehicle Conference, Paper No. 74-306 (1974).
U.S. Pat. Nos. 3,456,611 (Johnson) and No. 2,930,338 (Flomenhoft) also attempted to create a smooth-riding hydrofoil craft by attaching springs or cylinders to the vertical struts of hydrofoils. However, neither of these patents addresses the problem created by the added mass effect. Johnson employs his vertical struts as "equalizers" (to stabilize the craft) and shock absorbers, while Flomenhoft uses his struts for "better cushioning." Thus, it has proven extremely difficult to devise a hydrofoil craft which can compensate for the "added mass" effect of water so as to enable it to operate at high speeds in rough water.
With respect to WIG aircraft, the orbital water velocities are unimportant because these aircraft are not in water contact. However, WIG aircraft are still subject to many changes in the lift of their wings. When a wave crest passes under a wing, the proximity of the crest causes the wing lift to increase (at constant speed and pitch angle) and the subsequent trough causes the lift to decrease. Moreover, any head or following wind follows the contours of the waves, moving upwards toward each crest and downwards toward each trough. If the wind is blowing strongly, the vertical components of its velocity can also induce an increase or decrease in lift.
For example, a WIG aircraft which is cruising at 500 knots over water which has a wavelength of 200 feet experiences a vertical vibration at about ##EQU3## Clearly, a vertical vibration at this frequency could not be minimized by merely changing the wing angle of incidence or by cyclically moving the wing's trailing edge flaps to smooth out the lift vibrations. See generally Ellsworth, W., "Hydrofoil Development--Issues and Answers," AlAA/SNAME Advanced Marine Vehicle Conference, Paper No. 74-306 (1974). Thus, WIG aircraft, like hydrofoil craft, are subject to rough rides due to the changes in lift induced by the proximity of the sea's surface and by head or following winds.
Accordingly, there remains a need in the art for hydrofoil craft which can compensate for the random upgusts and downgusts of water velocity around its foils and which can maintain approximately constant lift so that the hull above the foils can ride smoothly at high speed in rough water. Furthermore, there also remains a need in the art for WIG aircraft which can compensate for the random changes in the lift of its wings so that the aircraft can fly comfortably just above the water's surface.